If you're using a folded joint then yes, keeping the joint as long as possible may be good.
But for my slot & tab joint method, I've found that it really doesn't matter where it is, as far as joint strength is concerned, because the interlocked slot and tabs are the same size wherever they are. The joint is usually at least half the depth of the cone, for the pans I've used, anyway; I can imagine a very tall pan with full-height handles might have less, but I don't have any such pans...
The other reason for keeping joint and handle together is that the handle opening provides a natural weak point in the entire structure, and, in stiffer foils that aren't 'encouraged' to hold their shape, the tips of the opening can tend to bow out away from the pan. If the opening and the joint are on opposite sides, you have two weaknesses in the cone circularity. The overlapping of the joint helps to keep this issue under control a little. I also usually keep the handle openings pretty tight, so care is needed when putting the pan in the cone. If the joint were on the opposite side, I'd have to take care not to pop the joint open whilst negotiating the pan into the cone.
It's always best to pre-bend the cone by rolling it up into a tighter cone, so that, when released, it relaxes into just about the right size cone to fit the pan, so that little or no encouragement is needed to make it form the right-sized cone. Concentrate especially on the area around the pan opening, as this is where the cone will tend to bow out, as the conic section is interrupted by the opening.
In the Flissure split version, there's no vertical joint at all in the upper section (which has confused a number of users of the script), so the ends of this must, by necessity, be at the handle opening... I find that the horizontal Flissure joint, when mated, allows the foil to act pretty much like a single piece of foil, due to the overlapping joint, and the conical shape which holds the joint securely in place; once formed into a cone, the Flissure joint cannot be pulled undone, because the base up the upper half conic is a larger diameter than the top of the lower half conic.
Have a play with this idea; you can tell the script to make a very shallow handle opening, and then make one with the required depth, and put the handle openings on the first template. Or you could just use the basic template and draw the opening by hand (shock horror!). You might find it works better than I have.